The (D) Property in Banach Spaces


Creative Commons License

Soybas D.

ABSTRACT AND APPLIED ANALYSIS, 2012 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Publication Date: 2012
  • Doi Number: 10.1155/2012/754531
  • Title of Journal : ABSTRACT AND APPLIED ANALYSIS

Abstract

A Banach space E is said to have (D) property if every bounded linear operator T : F -> E* is weakly compact for every Banach space F whose dual does not contain an isomorphic copy of l(infinity). Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V*) property of Pelczynski (and hence every Banach space with (V) property) has (D) property. We show that the space L-1(v) of real functions, which are integrable with respect to a measure v with values in a Banach space X, has (D) property. We give some other results concerning Banach spaces with (D) property.